Well, it's already a well-established principle that, when you take taxpayer money from the government, the government gets to attach conditions to it as they see fit. That's not a violation of any individual rights.
Regardless of your stance on this topic, this is a bad example. Regulating what teachers are allowed to tell students in the course of their employment as teachers is not a freedom of speech issue, any more than the owner of a fast food restaurant requiring their employees to upsell is a freedom of speech issue.
Yes, there are higher ideals in play in the first case, but that does not make it a freedom of speech issue, legally or even ethically. Employers can regulate what you say while working for them on their time, and that holds whether the employer is private or public.
Similarly biology teachers aren't allowed to teach intelligent design unless it is a part of the curriculum, you can't just teach whatever theory you want without the school boards permission.
I don't think that biology teachers should teach intelligent design, and I don't think that is a free speech violation.
conflates the topic of free speech, with state-funded education that teaches people they are automatically oppressed (privilege theory), and teaching to a captive audience (students).